Question

Which expressions are equivalent to the one below? log 2- log 8

Answer 1

Answer:

A and B

Step-by-step explanation:

Answer 2

Answer:

A. $\log (2)+\log (\frac{1}{8})$

B. $log (\frac{1}{4})$

Step-by-step explanation:

Given expression:

$\log 2-\log 8$

Using properties of logarithm we can write the expression in various equivalent forms:

1) Using quotient rule $[\log a-\log b=log \frac{a}{b}]$ :

$\log 2-\log 8$

⇒$log \frac{2}{8}]$

Reducing $\frac{2}{8}$ to simple fraction by dividing numerator and denominator by their greatest common factor.

⇒$log \frac{2\div 2}{8\div 2}]$

⇒$log \frac{1}{4}]$

2) Plugging in $\log 1$ in the expression as $\log 1=0$

⇒ $\log 2+\log 1-\log 8$

Using quotient rule again $[\log a-\log b=log \frac{a}{b}]$

⇒$\log 2+\log \frac{1}{8}$